Scalable high yield exfoliation for monolayer nanosheets

Although two-dimensional (2D) materials have grown into an extended family that accommodates hundreds of members and have demonstrated promising advantages in many fields, their practical applications are still hindered by the lack of scalable high-yield production of monolayer products. Here, we show that scalable production of monolayer nanosheets can be achieved by a facile ball-milling exfoliation method with the assistance of viscous polyethyleneimine (PEI) liquid. As a demonstration, graphite is effectively exfoliated into graphene nanosheets, achieving a high monolayer percentage of 97.9% at a yield of 78.3%. The universality of this technique is also proven by successfully exfoliating other types of representative layered materials with different structures, such as carbon nitride, covalent organic framework, zeolitic imidazolate framework and hexagonal boron nitride. This scalable exfoliation technique for monolayer nanosheets could catalyze the synthesis and industrialization of 2D nanosheet materials.

Note: The amount of added PEI mixture has direct impacts on the exfoliation of layered materials and the protection of exfoliated nanosheets. The impacts are discussed in detail in section 5.

Supplementary 1.3 Preparation of bulk materials
Graphitic Carbon Nitride: Bulk graphitic carbon nitride (g-C3N4) was prepared via a two-step calcination method 1 . Briefly, urea powder (10 g) was added to a crucible (100 mL capacity) with a cover (sealed with aluminum foil) and calcined at 550 °C for 2 h with a heating rate of 5 °C/min in a muffle oven under air condition. Then, the obtained faint yellow powder (1 g) was ground and filled into a crucible (same capacity) and calcined again under same condition. The final light-yellow powder was stored at room temperature before exfoliation experiments. washed by water and ethanol for two times. It is worthy to be mentioned that ZIF-L is not stable in aqueous environment without excessive Hmim although it was synthesized in water. Therefore, ethanol was chosen as the solvent for processing.

ZIF-L:
TAPB-PDA COF: COF powder (TAPB-PDA) was prepared according to a low temperature synthesis route catalyzed by metal triflates 3 . Briefly, Terephthalaldehyde (40 mg, 0.30 mmol) and 1,3,5-tris(4 aminophenyl)benzene (72 mg, 0.205 mmol) were added to a 25 mL scintillation vial in coupled with a 1,4-dioxane/mesitylene mixture (4:1 v/v, 16 mL). This mixture was first sonicated for 10 s and then heated to 70 °C for 5 minutes to ensure that all solids had dissolved, Scandium (III) trifluoromethanesulfonate (6 mg, 0.012 mmol) was added to the solution after temperature cooling back to room temperature, and it was then sonicated for 10 s immediately. The reaction solution was left without stirring for 2.5 h, and then a significant amount of brick red solid precipitate was obtained.
Two kinds of polymer liquids were tested as exfoliation assistants in our preliminary experiments.
After milling for 15h, graphite milling with PEI can be well dispersed in water, which is one of the important clues of effective exfoliation. Conversely, graphite milling with PEG-400 does not appear to be dispersible in water, which means an ultra-low exfoliation yield. The ineffectiveness of PEG-400 could be explained by the inefficient force transmission efficiency because of the low viscosity of PEG-400 (only at around 122 mPa·s, measured at 20 °C), or it could be its low adsorption energy on the graphene surface. However, our DFT calculation results found the adsorption energy of both PEI and PEG on graphene are greater than the interlayer binding energy of graphite (Supplementary   Table 5.1). The key difference between PEI and PEG on their properties are their viscosity, suggesting the crucial role of high viscosity in this sticky exfoliation strategy. Removing additives from nanosheet dispersion is usually time-consuming and lab-intensive in 2D materials synthesis. Vacuum-assisted filtration is one of the commonly adopted methods. However, it is only suitable for rinsing a small amount of 2D materials. This is because of the fact that 2D materials are prone to parallelly stacking with each other under the directional water flow and form a laminar film on filter 4 . This film not only dramatically reduces the rinsing efficiency but also blocks the additives from being washed out. Another method is dialysis. It, however, requires a large amount of water and is time-consuming as well.
In this work, we developed a rinsing process by taking advantage of membrane filtration. The membrane filtration set-up was designed to avoid solutes accumulating on the membrane surface so as to minimize concentration polarization. Briefly, 10 mL nanosheet dispersion was filled into a stainless-steel dead-end cell (HP 4750, Sterlitech, USA) under constant stirring to avoid agglomeration or forming a fine filtration cake. A nylon ultrafiltration membrane (pore size: 0.22 um, diameter 47 mm, Sterlitech, USA) was loaded at the bottom of the dead-end cell. The cell was connected with a 5 L tank with feed milli-Q water. They were connected with a gas cylinder with compressed N2. The rinsing process starts with charging the water into the cell (by opening valve B and closing valve A in Supplementary Fig 1.2) until the liquid level in cell reaches marker A (around 100 mL). Then by closing valve B and opening valve A (Supplementary Fig. 1.2), water with dissolved PEI molecules will flow out of the cell driven by a pressure gradient, while nanosheets are blocked inside the cell by the membranes. This process lasted until the water level in cell reached mark B (around 10 mL) before filling cell with water to mark A again. The rinsing needed to be repeated several times to adequately remove free PEI from nanosheet dispersion. It should be noted that for boron nitride and carbon nitride, we washed the nanosheets with 0.1M HCl three times followed by water to partially defunctionalize the nanosheets in order to ensure a better resolution for AFM characterization (Supplementary Section 4.2). Ethanol was chosen as the solvent for the rinsing of ZIF-L instead of water concerning its poor stability in water 5 . A UV-Vis spectrophotometer (UV-2600, Shimadzu) was adopted to detect the concentration of PEI in outlet water. In this work, we continued the resining step until the PEI concentration in outlet water is less than less than 0.0001 mg/mL. The rinsing method effectively mitigates nanosheet agglomeration, avoids the formation of laminar membranes, and achieves high removal of free PEI molecules.

Supplementary 1.6 Preparation of powder and liquid dispersions
After finishing rinsing, a certain amount of water was added to the cell to ensure the liquid volume was around 20 mL. The cell was then left stirring for 30 min. Although under continuous stirring, a filter cake still formed on the membrane during rinsing process. Therefore, the dispersion was then decanted to a beaker, the nylon membrane with a filter cake was taken out and put into a beaker as  Residual PEI molecules on graphene nanosheets were removed partially and totally to study their impacts on conductivity. For HCl-treated graphene films, 100-mL 0.1 M HCl was filtrated immediately after finishing the filtration of graphene dispersion, which was then followed by repeated filtration of 100 mL milli-Q water 5 times. This process can remove around 45% of residual PEI according to the results in supplementary Section 4.2. In an effort to completely remove residual PEI, the obtained thick free-standing graphene film was subject to a heat treatment described in supplementary Section 4.2. Interestingly, the graphene film can maintain its original shape without breaking into small pieces and the weight loss after the heat treatment is at around 10%, which is close to the percentage of residual PEI. In this work, although the heights of thin graphene nanosheets are a little higher than the theoretical thickness (0.335 nm), they are less than the thickness of bilayers graphene (0.74 nm) 9 . The higher thickness of graphene obtained here than theoretical thickness is fairly reasonable. This is because the residual PEI molecules (around 11.5 wt.%, Supplementary section 4.1) on graphene nanosheets can act as spacer between graphene and mica as well as between cantilever and graphene, contributing to the measured heights. According to our simulation results, single-layer graphene nanosheets adsorbed with one-layer PEI possess a thickness of 0.95 nm ( Supplementary Fig. 5.11A). Furthermore, the monolayer nature of the as-prepared graphene nanosheets is mutually supported by their Raman spectra and diffraction patterns, which are discussed in Supplementary Section 2.3. By following these lines of reasoning, we concluded that 91.2% of the obtained nanosheets are monolayer graphene, supporting the excellent exfoliation efficiency of this sticky ball-milling method. 400 nm to 1 µm, and 1 µm to 2µm with response to the milling time of 15 h, 10 h, and 5 h, respectively.
Interestingly, the obtained nanosheets are almost all in monolayer when milling for 15 h (only 11 pieces of multilayer sheets out of analyzed 522 pieces are not monolayered, corresponding to a monolayer percentage of 97.9%). Although the monolayer percentage decreases to ~76% as milling time is reduced to 5 h, the percentage is still much higher than most reported works as detailed in Supplementary leading to an increase in the apparent heights measured by AFM. What is interesting is that for graphene nanosheets exfoliated with 5-h milling, the apparent heights are around 0.5~0.6 nm. These heights are much lower than the theoretical thickness (0.67) and the observed thickness (0.74 nm) of bilayer graphene 9 , further confirming that the graphene obtained in this work are indeed monolayers.
Although for graphene obtained by 15-h milling, the heights (0.8-1 nm) overtake the thickness of bilayer graphene, we still believe that them are monolayers for the same reason. This is also under the assumption that the layer number of exfoliated nanosheets is not expected to increase with the extension of milling time. As we have confirmed that graphene nanosheets exfoliated by 5h and 10 h are mainly composed of monolayers, it is reasonable to take nanosheets obtained by 15-h milling are monolayers as well. To provide further evidence for validating that the small discs spotted by AFM are graphene nanosheets, we tried to correlate the AFM morphology imaging with Raman structure mapping.
Graphene fabricated from 15-h milling was deposited on mica following the same procedures of AFM sample preparation and used for demonstration. Since our nanosheets were not easily observed by Raman and AFM optical microscope, we manually marked our sample with 9 points to help us locate the same area in two separated characterization devices. The AFM characterization was firstly performed to find nanosheets around these points. As shown in the Supplementary Figure 2.5C, small discs were found in the area 1, 2, 3 with their thickness at around 1 nm and lateral size around 200 nm similar to what we found previously from AFM (Supplementary Fig. 2.5A). Once nanosheets were spotted in the vicinity of one of these points, Raman spectroscopy was then utilized to generate spectra from the same area with the help of our point markers on mica (Supplementary Fig. 2.5B).
Repletely accumulated Raman signals indicate that there are plenty of pieces of graphene in these areas with identifiable typical D, G, 2D Raman peaks of graphene. All Raman patterns feature a symmetrical 2D band, suggesting the high monolayer percentage 11,12 . Besides, the intensity ratios of I2D/IG of these generated Raman patterns locate in the range of 1.06-3.1 (Supplementary Fig. 2.5C).
Giving that the I2D/IG band ratio is lower than 1 for bilayer graphene, and the ratio decreases with the increase of layer number 12 . In this line of reasoning, we conclude that the sub-nm discs observed by AFM are monolayer graphene. Furthermore, the ID/IG band intensity, which is related to sp 3 carbon defects, is in the range of 0.3-0.5. Such a low ID/IG ratio originated from the quality lattice is much lower than that of graphene oxide (GO) and reduced GO (rGO) (~0.7-0.9) 13 , but is comparable to high-speed mixing delivered vacancy-defect-free few-layer graphene (0.17-0.37) 14 . When graphene nanosheets were deposited on a porous AAO disc, large nanosheets in the middle (yellow cycle) displaying a clear shape were observed. Although some small nanosheets can pass through the AAO disc that has a pore size similar to theirs, upon close observation, we still found The morphology difference between monolayer and multilayer nanosheets could be the result of the in-plane breaking processes. Initial delamination and breaking start from structural deformation at mechanically vulnerable crystalline structural deformations on material surface, often named "kind band striations" 15,16,17 . This crystalline structural breaking leads to incompletely exfoliated few-layer nanosheets with large sizes and sharp edges. The large nanosheets then undergo further in-plane breaking by collisions of protruding sharp ridges on the grinding ball surface (Fig. 3b), which provides sufficiently high compression to break graphene nanosheets at any point due to concentrated forces. Considering the highly random distribution of these ridges over the balls, the long edges of the nanosheets have a better chance to be trimmed than short edges during milling, as a result, smaller nanosheets that have undergone more times of breaking tend to be more likely to end up with higher roundness but with serrated edges.

Supplementary 2.5 Comparison with other non-chemistry synthesis methods
We have compared the sticky milling method with other scalable non-chemistry synthesis methods in terms of yield, lateral size, thickness, and monolayer percentage. The aspect ratio was calculated according to the averaged size and layer number reported in these references. However, some references only provided AFM measured heights, so we list the heights as provided instead of layer number. Hence, aspect ratios are given as nm/nm instead of nm/per layer for these cases. Few-layer graphene was obtained in most cases with the aspect ratio of graphene less than 500 nm/nm. Only two papers claimed that they got monodispersed single-layer graphene. One used salt-assisted ball milling to give graphene with a low yield at around 10% and small lateral size (~300 nm), and the other was Flash joule heating which was performed under ultrahigh temperature. Our method can produce graphene nanosheets with an actual yield of ~78.3 % and monolayer contents of over 90%.
By applying short-time milling, the lateral size of obtained monolayer graphene can reach an average of 1640 nm (Supplementary Fig. 2.3).   The scale described in the main text used four 250 mL milling jars, and 0.5 g graphite was mixed with 2 g PEI in each jar. The ultra-high yield of the method and excellent quality of the resultant graphene were demonstrated as above. Sale-up studies were conducted by using 500 mL milling jars.

Supplementary
We found that with more graphite added to the milling jars, less PEI was needed to ensure a decent yield (Supplementary Table 3.1). The PEI:graphite ratio could be lowered to 1:2 when 20 g graphite was added. The obtained nanosheets at the scale of 20-g graphite were analyzed in terms of size and thickness by AFM. Their lateral sizes (around 200 to 500 nm) are quite close to those of graphene nanosheets fabricated at small scale. The thickness of the graphene nanosheets indicated by AFM height profile shows 90% of them at around 1 nm, meaning they are monolayer as well ( Supplementary Fig. 3.1).
Since there are four jars in this mill, 80 g graphite can be processed in one batch. Hence, 41g monolayer graphene was produced using the lab-scale ball milling machine. Considering that 15 h is taken for each batch, it gives a production capacity of ~2.74 g/h (~65.8 g/day). This means that only 20 lab-scale ball milling machines are needed to achieve a production capacity of kilogram-scale, which is needed for various industrial applications of graphene 40 . Given ball milling is a commonly used technology in industry with various scales, it is reasonable to believe that the sticky milling method has a great potential for large-scale production of high-quality monolayer graphene nanosheets. It should be noted that it is not feasible for mass production by simply multiplying the loading amount of graphite and PEI. The ratio of graphite to PEI is a key factor that should be carefully optimized when scaling up this method on practical occasions.  For convenient storage and distribution, it is highly desired for graphene products to be processed into powder form. Graphene prepared by liquid phase exfoliation usually relies on organic solvents as a suspension medium, which causes inconvenience in practical storage, transport and distribution 41 .
To combat this, it is meaningful to explore whether the graphene nanosheets synthesized in this study can be processed into powder for storage and distribution, and then re-dispersed for late use. To achieve this, powder of graphene was first obtained by freeze-drying graphene water dispersion with a concentration of 2 mg/ml. The powder was then kept in a plastic or glass sample container in an ambient environment. The powder shows an extremely fluffy texture with a noticeable increase in volume compared to the graphite raw materials (Fig. 1a  Although graphene in powder is ideal for storage and transport, liquid form is widely needed in material processing, e.g., mixing, filtration, coating and inkjet printing, and so on. Hence, a more important property of the synthesized graphene nanosheets is whether they can be re-dispersed in a liquid medium after they are dried forming powder. After the graphene powder (exfoliated with PEI Vis-5, milling time 15h) was kept under the ambient environment for three months, we tried to redisperse them using different solvents. Briefly

Supplementary Section 4. Residual PEI Supplementary 4.1 Concentration of residual PEI
Graphene powder samples were prepared by freeze-drying the water dispersions after water rinsing.
An elemental analyzer (FlashSmart, Thermo Scientific) was adopted to analyze the weight ratio of elemental content (C, N, and H) in these graphene powder samples synthesized at different exfoliation time. In this work, we mainly focused on the weight ratio of N, which is only contributed from PEI.
The N content of PEI Vis-5 is of 31.95 wt.%. Therefore, the weight ratio of residual PEI on graphene can be obtained through simple calculation. As shown in Supplementary  Figure 4.1, the weight ratio of residual PEI increases along with milling time, but slowly levels off. We speculate that PEI molecules were grafted or bonded onto graphene nanosheets largely due to the fragmentation and breaking of graphite. When graphite breaks caused by the crashing or shearing effects of grinding balls, numerous active C atoms are created along newly formed edges due to the breaking of C-C bonds. These active C atoms can react with amino groups of PEI molecules driven by high mechanical energy, forming strong covalent bonds 42 .

Supplementary 4.2 Removal of residual PEI
Although residual PEI on graphene nanosheets offers great convenience in storage and redispersion, they may be not desirable on some occasions. Therefore, two methods were explored in this study to remove residual PEI molecules. PEI is a polycation and its ionization strongly depends on pH 43 .
Normally, the higher the ionization degree, the better the solubility in water. In light of this, the first method is acid treatment. In this method, graphene (exfoliated with Vis-5 for 10h) dispersion was diluted in 0.1M HCl solution to a concentration of 0.1 mg/mL. The solution then was put on a shaker overnight and followed by thoroughly washing with Milli-Q water. After being re-dispersed in water and freeze-dried, the as-obtained graphene powder was characterized by an Elementar Vario EL III elemental analyzer in terms of its elemental composition, in particular, the element weight ratio of N. Apart from elemental analysis, the removal of PEI functionalities was also investigated by X-ray photoelectron spectroscopy (XPS). Full XPS survey scans of pristine graphene powder, de-   Graphene obtained by 10-h milling with PEI Vis-5 was chosen for fabricating conductive films.

Supplementary 4.3 Conductivity of graphene nanosheets Supplementary
Graphene water dispersion was diluted to a concentration of 0.01 mg/mL and then was vacuumassisted filtrated on PES substrate membranes. The thickness was controlled by varying the loading density. A source meter equipped with a four-point probe was applied to measure the sheet resistance of the obtained films. For thin membrane like sample 1, the conductivity was measured with the PES substrate. For thicker films, free-standing graphene films were obtained by following a freeze-andsublimation transfer strategy 6 . Noted that graphene loading density of samples 3, 4, 5 is at the same level but with different post-treatments. The obtained films showed different thicknesses. The PEI functionalities were partially and totally removed to study its impacts on film conductivity.

Supplementary 4.4 Zeta potential of synthesized nanosheets
Zeta potential of the exfoliated nanosheets (graphene, BN and g-C3N4) was tested from their diluted water dispersion at a concentration of 0.05 mg/mL. Free PEI molecules were washed out before testing. pH of these solutions was also measured. All Zeta potential tests were performed directly using the water dispersion without pH adjusting. Because of residual PEI, the exfoliated graphene, h-   Fig. 4.3). The decreased ion transport rate and divalent/monovalent ion selectivity emphasize the main roles of PEI in the laminar membrane 4, 59, 60 : (1) acting as molecular spacers to increase the mass transport rate; (2) regulating ion transport by the Donnan effect.

Supplementary Section 5. Exfoliation mechanism Supplementary 5.1 Graphene at intermediate stage
To understand the exfoliation mechanism, graphene obtained from 1-h and 2-h milling was deposited on mica by following the same AFM sample preparation procedures excepting without centrifugation.
We found that both thin-yet-large and thick-yet-small nanosheets exist in the exfoliation products at 1-1 and 2-h ( Supplementary Fig. 5.1). The absence of large and thick particles could be the result that they are prone to precipitation and thus being excluded during sample preparation process. Along with the milling time increasing to 2 h, the lateral size of the nanosheets narrows down to 1 to 2 µm, and their thickness reduces to less than 100 nm ( Supplementary Fig. 5.1).
According to these results, the proposed exfoliation and material breaking mechanism presents as follows. Starting from thick and large particles, the in-plane breaking and out-of-plane delamination occur simultaneously on them at the initial stage driven by grinding effects. The delamination process where vi and i are the translational and rotational velocities of particle i, and Ii (= 2 2 /5) is the moment of the inertia of the particle. The forces involved are: the gravitational force mig and the forces between particles (and between particles and walls) which include the elastic force fe,ij, damping force fd,ij, viscous force fvis,ij and the cohesive force fc,ij. The torque acting on particle i due to particle j includes two components: Tt,ij generated by the tangential force and Tr,ij generated by asymmetric normal contact force. If particle i undergoes multiple interactions, the individual interaction forces and torques are summed up for all particles interacting with particle i. In this work, the cohesive force is the capillary force due to the liquid PEI. The model for the capillary force considering the normal and tangential viscous forces is adopted here 64 . Most of the equations have been well established as, for example, reviewed by Zhu et al 65 .
To accommodate the complicated geometry boundary and the rotational motion of the mill, an inhouse DEM package is used 62 . Meshes are generated for the mill, and the contacts between the mill and particles can be detected and treated similarly to particle-particle contacts. The DEM package has been applied to different granular systems and proved to work 62, 63, 66 .

Supplementary 5.2.2 Parameters for the DEM simulation
The geometry of the mill is set according to the 250 mL milling jar where the diameter is 80 mm and the height 78 mm. The revolution speed is set as 500 rpm. Three sizes of the grinding balls (10 mm, To simplify the calculation, we kept the moving behavior of grinding balls constant when analyzing the system with and without PEI addition. In order to verify the reliability of this assumption, we did a comparison of the transitional velocity distribution of grinding balls with adding water and PEI respectively. It is noted that the systems with water and PEI have a similar distribution. The system with PEI has obvious fluctuations between the two peaks which could be the result of increased viscous energy dissipation. This difference is expected to have little effect on the exfoliation. Although the balls look glossy on the surface, there are actually highly rough on the surface. There are many micron-scale holes on the surface that can be seen by optical microscope ( Supplementary   Fig. 5.6B). An optical profilometer (Contour GTI 3D optical profiler, Bruker) was adopted to give more details of the milling-ball surface. The largest grinding balls (d=10 mm) were chosen for the characterization. The results show that the surface presents as a ridge-and-valley structure. Statistical analysis of 50 peaks on the height profile along the black line in Supplementary Figure 5.5C shows that the half peak width of these tips is average at 1.6 µm, the height of these tips is averaged at 0.388 µm, and the distance between neighboring tips is averaged at 2.92 µm. To evaluate the influence of PEI:graphite ratio, the amount of PEI was adjusted with other parameters keeping consistent (PEI Vis-5, milling time 15h). Only amorphous carbon nanoparticles without distinct 2D characteristics were observed when milling graphite alone ( Supplementary Fig. 5.7A).

Supplementary 5.3 Surface morphology characterization of grinding balls
When the PEI:graphite ratio was set as 2, the obtained nanosheets exhibited a thickness of ~0.6 nm ( Supplementary Fig. 5.7B), indicating they are monolayer graphene. However, their lateral size shows a broad distribution from tens of nanometers to hundreds of nanometers. This is the result that inefficient protection of PEI to graphene nanosheets from inadequate PEI addition. When we increased PEI addition to 8 times of graphite, the lateral size of graphene increased by 2 to 4 times to ~400-800 nm. However, their thickness only reduced to 1.5 to 1.7 nm ( Supplementary Fig. 5.7C), meaning inefficient exfoliation when adding excessive PEI. This phenomenon can be well described by our two-plane model. Excessive PEI buffer layer can provide effective protection to nanosheets, which enables graphene with a decent lateral size. However, according to equation (1) in the main text, shear force F is inversely proportional to the thickness of buffer layer Y, which means the thicker the buffer layer, the smaller shear force applied on graphite for exfoliation. As a consequence, 8 times addition of PEI is only able to exfoliate the graphene to ~1.5 nm in a period of 15 h. The results indicate that there is an optional PEI:graphite ratio.

Supplementary 5.5 Density Functional Theory (DFT) calculation Supplementary 5.5.1 Calculation methods
We performed density functional theory (DFT) calculation using the Vienna ab initio simulation package (VASP) 67,68 . The Perdew, Burke, and Ernzerhof (PBE) 69 exchange-correlation functional and the projector augmented wave (PAW) approach were adopted 70 . The DFT-D3 semi-empirical method is used to describe the weak dispersive force 71 . In our DFT calculations, the plane wave basis set cutoff energy was 400 eV. The energy convergence criterion was set to be 10 -4 eV, and the residual forces in the converged structures are smaller than 0.01 eV/Å. The valence atomic configurations are 4p 6 5s 1 4d 5 for Mo and 5p 6 6s 2 5d 4 for W. A vacuum space in z direction was larger than 10 Å to minimize the spurious interactions between the periodically repeated images. The model size of the monolayer supercell of 2D materials was greater than 30 Å × 30 Å and a Γ-centered 1×1×1 k-point mesh was used for the PEI/PEG adsorption on 2D materials monolayer. The k-point grid was 3 × 3 × 1 for the bulk and bilayer of the 2D materials. At a chosen relative top layer displacement, the x and y coordinates of all atoms were fixed and only the z coordinate was relaxed to generate the potential energy surfaces. In the cases of C3N4 and COF, the bilayers were set as rigid layers to avoid structural deformation during the sliding motion  The potential energy surfaces of 2D materials show three-fold symmetry, and the bigger gradient means larger interface shearing force. Therefore, we can calculate the ISS value through the sliding direction which has the lowest gradient ( Supplementary Fig. 5.8). The ISS ( ) is defined as where is the shearing force in the sliding process, is the area of 2D materials bilayer, is the total energy of 2D materials bilayer in the sliding process, and is the sliding displacement of the top layer.
According to formula (5.5) and (5.6), we estimated the range of ISS value of these layered materials is 0.116 bilayer graphene (Supplementary Table 5.2), which is close to the previous reported 0.1 Gpa 72,73 . The ISS values are smaller than the experimental shear force the sticky milling can achieve, so mechanical exfoliation is energetically possible.  The results suggest a small amount of monolayer graphene can be obtained by PEI with a viscosity of around 7235 mPa·s. However, a viscosity of over around 16,858 mPa.s is needed to achieve a total monolayer product. We therefore take 7235 mPa·s as the viscosity threshold, by which only the viscosity of the exfoliation liquid over this threshold can be seen as sticky exfoliation. The viscosity of the exfoliation liquid under this threshold is not suitable for the production of monolayer graphene, which could be the reason for the failure of achieving high monolayer percentage by traditional LPE methods. mPa.s). It is worthy to note that the viscosity of PEI mixture was measured at room temperature (20 °C). To understand the deviation between theoretical calculation and experimental results, we measured the in-situ temperature of the milling jar using an infrared thermal camera right after 5

Supplementary
hours of exfoliation at 500 rpm. We found that the temperature of PEI mixture during exfoliation process was around 50 °C. As shown in Supplementary  However, ZIF-L nanosheets are not stable as they can easily transform to ZIF-8 particles in organic solvents or by heating according to previous research 5 . We also noted this transformation process from TEM images of two nanosheets in two different phase transformation status from a same sample (Supplementary Fig. 6.3). This transformation can be evident from XRD patterns of the exfoliated nanosheets as well, which shows the characteristic peaks at 2θ of 7.3°, 12.7°, and 18.0°, corresponding to the (011), (112) and (222) planes of the structure of ZIF-8 ( Supplementary Fig. 6.4). Exfoliation of g-C3N4 by sticky exfoliation method was also studied. The exfoliated g-C3N4 nanosheets can be finely dispersed in water similar to the case of graphene. Unlike graphene, g-C3N4 water dispersion presents as a light-yellow dispersion instead of black one. The XRD patterns of exfoliated g-C3N4 show the characteristic peaks including (002), (100), but these peaks are broader and with reduced intensities compared to that of bulk powder, indicating its reduced size and thickness. The SEM and TEM images confirm the lateral size reduces from several microns to hundreds of nanometers (averaged at 275 nm). AFM statics show that almost all the thickness of the observed nanosheets is less than 1nm with deviations less than 0.2 nm, indicating an ultrahigh percentage of monolayers contained in the obtained products.
In summary, the developed sticky milling is suitable for the exfoliation of TAPB-PDA COF, g-C3N4 and ZIF-L. The SEM, AFM and TEM images confirm that the lateral size and thickness of these layered bulk materials were downsized to hundreds of nanometers and thickness reduced to sub-1 nm region with deviations within 0.3 nm (Supplementary Figs. 6.1, 6.2, 6.5). The heights of these nanosheets display an ultra-narrow unimodal distribution, which is obviously different from previously observed normal distribution in terms of heights in other mechanical exfoliated products 41,53 . This could be the sign that the thickness of most nanosheets has been adequately reduced and has reached a limit. Furthermore, based on our experimental and simulation experience gained from the exfoliation of graphene and h-BN, the apparent heights of monolayered graphene locate in the range of 0.5 nm to 1 nm. Both the nanosheets and the residual PEI contribute to the observed apparent heights by AFM. We, therefore, take the nanosheets of g-C3N4, TAPB-PDA COF, ZIF-L with their thickness less than 1 nm as monolayers. From AFM statistics, these layered crystals can all be exfoliated into nanosheets with a high monolayer percentage of over 85%. The results consolidate the universality of this sticky exfoliation method for the production of monolayer nanosheets.  TEM, SEM and AFM statistics were applied to study the exfoliation efficiency. Unfortunately, AFM results show that an averaged thickness of h-BN nanosheets was as high as 7 nm and the percentage of monolayer nanosheets is only ~5% (Supplementary Fig. 6.10A). We assume that it could be the result of the much more intensive interlayer attraction force, and thus more difficult for exfoliation and stronger propensity to re-staking 74 . In order to understand how these multilayer h-BN nanosheets are formed, converged beam electric diffraction (CEBD) which focuses on a small area was performed to study these multilayer nanosheets. We found there seem to be two kinds of multilayer BN. One looks like that it is piled up by several pieces of BN nanosheets as shown in Supplementary   Figure 6.8A. Although it shows as a multilayer BN, the diffraction pattern obtained on the edge of the nanosheet displays as a monolayer BN fingerprint (brighter inner spots than the outer spots). The results indicate that the observed BN sheet may consist of a piling of several monolayers. As a contrast, another kind of nanosheet that looks like an individual nanosheet but displays a typical diffraction pattern of multilayer BN with more intense outer spots than inner spots ( Supplementary Fig 6.8B).

Supplementary 6.2 Exfoliation of BN Supplementary
This kind of multilayers may result from unsuccessful exfoliation. Therefore, we reckon that multilayer h-BN nanosheets may either come from restacking of nanosheets or those that have not been fully exfoliated.   41 .
In summary, although bulk BN cannot be exfoliated to give a totally monolayered product, the monolayer percentage can be promoted from ~5% (BN-1) to ~14% (BN-2) by prolonging the milling time, and it can be further promoted to ~57% (BN-3) by applying higher milling rotation speed (Supplementary Figs. 6.10). This high monolayer percentage still shows superiority to other mechanical exfoliation methods as detailed in Supplementary Section 6.3. Note: There are hardly papers focusing on the monolayer percentage contained in their exfoliated products. For papers with thickness distribution data, we take the percentage of nanosheets with the thinnest thickness in the sub-nm region as the monolayer percentage in order to give a fair comparison.